Speaker: Daniel Stern, University of Chicago

Title: Existence theory for harmonic maps and connections to spectral geometry

Abstract: I’ll discuss recent progress on the existence theory for harmonic maps, in particular the existence of harmonic maps of-optimal regularity from manifolds of dimension n>2 to every non-aspherical closed manifold containing no stable minimal two-spheres. As an application, we’ll see that every manifold carries a canonical family of sphere-valued harmonic maps, which (in dimension<6) stabilize at a solution of a spectral isoperimetric problem generalizing the conformal maximization of Laplace eigenvalues on surfaces. Based on joint work with Mikhail Karpukhin.

Engineering and Computer Science West (ECSW), 1.315
800 W. Campbell Road, Richardson, Texas 75080-3021

Natural Sciences & Mathematics

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